Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.6 Phase Shift; Sinusoidal Curve Fitting - 6.6 Assess Your Understanding - Page 430: 39

Answer

The amplitude ($A$) shows the maximum distance of the graph from its central line (its average value).Hence if the graph is not shifted vertically (the central line is the x-axis), then the vertical window should be at least $[-A, A]$ to include the whole graph. The horizontal scale depends on the number of periods required ($p$), and if $t=0$ is the starting point. To show at least two periods, starting at $t=0$, the horizontal window should be at least $[0, 2p].$

Work Step by Step

The amplitude ($A$) shows the maximum distance of the graph from its central line (its average value).Hence if the graph is not shifted vertically (the central line is the x-axis), then the vertical window should be at least $[-A, A]$ to include the whole graph. The horizontal scale depends on the number of periods required ($p$), and if $t=0$ is the starting point. To show at least two periods, starting at $t=0$, the horizontal window should be at least $[0, 2p].$
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